I learned “I am an American” in Camp Fire Girls in 1969 or 1970. But I don’t think the author of the quote is unknown. (Which is what the sites with the version I learned said.) I think we changed the quote and, so, the author didn’t really say it. The original, according to the first source I found was/said:
Prime Minister John Diefenbaker said on July 1, 1960:
I am a Canadian, a free Canadian, free to speak without fear, free to worship God in my own way, free to stand for what I think right, free to oppose what I believe wrong, free to choose those who shall govern my country. This heritage of freedom I pledge to uphold for myself and all mankind.
Despite the fact that it was probably a Canadian who originally said it, I believe it about the United States with all my heart.
And I am grateful to God and those who made it possible, that I live in such a blessed country.